Theorems · Theorem · ring theory
Algebra.sInf_toSubmodule
∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
(S : Set (Subalgebra R A)), Subalgebra.toSubmodule (sInf S) = sInf (⇑Subalgebra.toSubmodule '' S)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
- Subalgebrastatement and proof · cited by 1,353
- Set.iInterproof · cited by 1,084
- InfSet.sInfstatement and proof · cited by 935
- OrderEmbeddingstatement · cited by 619
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.